clear
clc
close all
% Listing 15.07 Integrating rocket velocity
v =[ 0.0 15.1 25.1 13.7 22.2 41.7 ...
    39.8 54.8 57.6 62.6 61.6 63.9 69.6 ...
    76.2 86.7 101.2 99.8 112.2 111.0 ...
    116.8 122.6 127.7 143.4 131.3 143.0 ...
    144.0 162.7 167.8 180.3 177.6 172.6 ...
    166.6 173.1 173.3 176.0 178.5 ...
    196.5 213.0 223.6 235.9 244.2 244.5 ...
    259.4 271.4 270.5 294.5 297.6 ...
    308.7 310.5 326.6 344.1 342.0 358.2 362.7 ];
lv = length(v);
dt = 0.2;
t = (0:lv-1) * dt;
h = dt * cumsum(v);
plot(t, v, t, h/5)
legend({'velocity’ ‘altitude/5' })
title('velocity and altitude of a rocket')
xlabel('time (sec)'); ylabel('v (m/s), h(m/5)')
fprintf('cumsum height: %g\n', h(end) );
fprintf('trapezoidal height: %g\n', ...
       trapezoid(v, t(1), t(end) ));
fprintf('Simpson''s Rule height: %g\n', ...
         simpson(v, t(1), t(end) ));
